This proposal is for the continuation of several research projects that use mathematical modeling to integrate and interpret experimental findings so that a better understanding of kidney function be can attained. More specifically, this proposal is directed to understanding renal processes that exhibit complex dynamic behaviors and/or complex spatial interactions, at the levels of microvessels, tubules, and nephron populations. Hypotheses for renal hemodynamic control will be tested by analyzing the coupling of the tubuloglomerular feedback (TGF) oscillator with vasomotion of the afferent arteriole (AA) and with adjoining TGF oscillators, by constructing a minimal dynamic and spatially distributed model of the AA to study the coordination and propagation of vasoconstriction arising from major determinants of vaso-activity, and by constructing a detailed model of nitric oxide action on vessel walls to determine its role in maintaining total segmental resistance. Hypotheses for the urine concentrating mechanism will be tested by analyzing the single-solute avian mechanism and by investigating potential mammalian inner medullary mechanisms that operate via descending limb hypertonicity. The principal mathematical methods that will be employed are explicit analysis, numerical methods for solving ordinary and partial differential equations, and the immersed boundary technique. The nature of the inner medullary urine concentrating mechanism remains an unsolved mystery of normal renal function. Many disorders of whole-body water balance result from inappropriate or deranged regulation of the concentrating mechanism. The afferent arteriole and the juxtaglomerular apparatus are major regulatory sites for blood flow and nephron load. A more complete analysis of the influences that come to bear at these sites, and their interactions, could greatly enrich our understanding of blood pressure control and renal electrolyte management. Moreover, these intrarenal control processes are deranged in several important renal diseases, including hypertension and diabetes, which are major causes of chronic renal failure in humans.